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Physical Review A

Comparison of quantum advantage experiments using random circuit sampling

Sangchul Oh, Sabre Kais

Published Feb 13, 2023• 3 citations
Publisher

Abstract

Random circuit sampling, the task of sampling bit strings from a random unitary operator, has been implemented to demonstrate quantum advantage on the Sycamore quantum processor with 53 qubits and on the Zuchongzhi quantum processor with 56 and 61 qubits. Recently, it was claimed that classical computers using tensor network simulation could catch on to current noisy quantum processors for random circuit sampling. While the linear cross-entropy benchmark fidelity was used to certify all these claims, it may not capture statistical properties of outputs in detail. Here, we compare the bit strings sampled from classical computers using tensor network simulation by Pan et al. [F. Pan, K. Chen, and P. Zhang, Phys. Rev. Lett. 129, 090502 (2022)] and by Kalachev et al. [G. Kalachev, P. Panteleev, P. Zhou, and M.-H. Yung, arXiv:2112.15083] with the bit strings from the Sycamore quantum processor. It is shown that all of Kalachev et al.'s samples passed the NIST random number tests. The heat maps of bit strings show that Pan et al.'s and Kalachev et al.'s samples are quite different from the Sycamore or Zuchongzhi samples. The analysis with the Marchenko-Pastur distribution and the Wasssertein distances demonstrates that Kalachev et al.'s samples are statistically closer to the Sycamore samples than Pan et al.'s while the three datasets have similar values for the linear cross-entropy fidelity. Our finding implies that further study is needed to certify or beat the claims of quantum advantage using random circuit sampling.

DOI
10.1103/physreva.107.022610

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Random circuit sampling, the task of sampling bit strings from a random unitary operator, has been implemented to demonstrate quantum advantage on the Sycamore quantum processor with 53 qubits and on the Zuchongzhi quantum processor with 56 and 61 qubits. Recently, it was claimed that classical computers using tensor network simulation could catch on to current noisy quantum processors for random circuit sampling. While the linear cross-entropy benchmark fidelity was used to certify all these claims, it may not capture statistical properties of outputs in detail. Here, we compare the bit strings sampled from classical computers using tensor network simulation by Pan et al. [F. Pan, K. Chen, and P. Zhang, Phys. Rev. Lett. 129, 090502 (2022)] and by Kalachev et al. [G. Kalachev, P. Panteleev, P. Zhou, and M.-H. Yung, arXiv:2112.15083] with the bit strings from the Sycamore quantum processor. It is shown that all of Kalachev et al.'s samples passed the NIST random number tests. The heat maps of bit strings show that Pan et al.'s and Kalachev et al.'s samples are quite different from the Sycamore or Zuchongzhi samples. The analysis with the Marchenko-Pastur distribution and the Wasssertein distances demonstrates that Kalachev et al.'s samples are statistically closer to the Sycamore samples than Pan et al.'s while the three datasets have similar values for the linear cross-entropy fidelity. Our finding implies that further study is needed to certify or beat the claims of quantum advantage using random circuit sampling.
Random circuit sampling, the task to sample bit strings from a random unitary operator, has been performed to demonstrate quantum advantage on the Sycamore quantum processor with 53 qubits and on the Zuchongzhi quantum processor with 56 and 61 qubits. Recently, it has been claimed that classical computers using tensor network simulation could catch on current noisy quantum processors for random circuit sampling. While the linear cross entropy benchmark fidelity is used to certify all these claims, it may not capture in detail statistical properties of outputs. Here, we compare the bit strings sampled from classical computers using tensor network simulation by Pan et al. [Phys. Rev. Lett. 129, 090502 (2022)] and by Kalachev et al. [arXiv:2112.15083 (2021)] and from the Sycamore and Zuchongzhi quantum processors. It is shown that all Kalachev et al.'s samples pass the NIST random number tests. The heat maps of bit strings show that Pan et al.'s and Kalachev et al.'s samples are quite different from the Sycamore or Zuzhongzhi samples. The analysis with the Marchenko-Pastur distribution and the Wasssertein distances demonstrates that Kalachev et al.'s samples are statistically close to the Sycamore samples than Pan et al.'s while the three datasets have similar values of the linear cross entropy fidelity. Our finding implies that further study is needed to certify or beat the claims of quantum advantage for random circuit sampling.
Random quantum circuit sampling, a task to sample bit strings from a random quantum circuit, is considered a suitable benchmark task to demonstrate the outperformance of quantum computers even with noisy qubits. Recently, random quantum circuit sampling was performed on the Sycamore quantum processor with 53 qubits [Nature (London) 574, 505 (2019)] and on the Zuchongzhi quantum processor with 56 qubits [Phys. Rev. Lett. 127, 180501 (2021)]. Here, we analyze and compare the statistical properties of the outputs of the random quantum circuit sampling by the Sycamore and Zuchongzhi processors. Using the Marchenko-Pastur law of random matrices of bit strings and the Wasssertein distances between bit strings, we find that the statistical properties of Sycamore bit strings are quite different from those of Zuchongzhi bit strings, while both processors score similar values of linear cross-entropy fidelity for random circuit sampling. Some bit strings sampled by the Zuchongzhi processor pass the NIST random number tests while both Sycamore and Zuchongzhi processors show similar patterns in the heat maps of bit strings. Zuchongzhi bit strings are much closer to classical uniform random bits than those of Sycamore. It is shown that the statistical properties of bit strings of both random quantum circuits change little as the depth of the random quantum circuits increases. Our findings raise a question about the computational reliability of noisy quantum processors because two quantum processors with similar noise levels and similar qubit structures produced statistically different outputs for the same random quantum circuit sampling.
Quantum supremacy has been recently reported for random circuit sampling on the Sycamore processor with 53 qubits. Here, we analyze the statistical properties of bit strings sampled from random quantum circuits. In contrast to classical random bit strings, bit strings sampled from Sycamore random circuits give rise to heat maps with stripe patterns at specific qubits, have more bit 1 than 0, and do not pass the NIST random number tests. The difference between the Sycamore bit strings and classical random bit strings is also demonstrated by the Marchenko-Pastur distribution and the Girko circular law of random matrices. The calculation of Wasserstein distances shows that the Sycamore bit strings are farther from bit strings sampled from Haar-measure random quantum circuits than classical random bit strings. Our results show that random matrices and Wasserstein distances could be used to analyze the performance of quantum computers.
We report forward random-circuit sampling (RCS) on the 120-qubit Nighthawk r2 superconducting processor (ibm_phoenix) with square-lattice connectivity, using 61 qubits, native CZ gates, and the standard cloud execution stack with no benchmark-specific calibration. Two independent fidelity estimators---mirror benchmarking and three- and four-patch cross-entropy benchmarking (XEB)---agree with each other at every measured depth, the mirror from 4 to 40 cycles and the patched estimators from 20 to 40 cycles, across more than two orders of magnitude of fidelity decay, and exceed the first-generation Nighthawk r1 device by more than an order of magnitude at fixed depth. The 36-cycle circuits sit at the depth where tensor-network contraction cost saturates at system size: a contraction-cost estimator validated against the published Sycamore and Zuchongzhi networks places the single-amplitude cost at ∼\sim∼102210^{22}1022 complex operations. At FXEB(36)=2.3×10−3F_{\mathrm{XEB}}(36)=2.3\times10^{-3}FXEB​(36)=2.3×10−3 under favorable memory assumptions this implies 1.2×10271.2\times10^{27}1.2×1027 machine operations within the bounded-fidelity rejection-sampling model --- more than a century of runtime on the Frontier supercomputer --- to collect a 10610^{6}106-sample ensemble, which takes only 19\,s on Nighthawk r2. To our knowledge, this is the first demonstration of quantum advantage for a vanilla random-circuit sampling on a commercially and broadly accessible quantum processor that most non-expert quantum computer users can easily replicate.
Leapfrogging Sycamore: Harnessing 1432 GPUs for 7×\times× Faster Quantum Random Circuit Sampling
Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical simulation time and challenged the claim of the first-generation quantum advantage experiments. However, in terms of generating uncorrelated samples, time-to-solution, and energy consumption, previous classical simulation experiments still underperform the \textit{Sycamore} processor. Here we report an energy-efficient classical simulation algorithm, using 1432 GPUs to simulate quantum random circuit sampling which generates uncorrelated samples with higher linear cross entropy score and is 7 times faster than \textit{Sycamore} 53 qubits experiment. We propose a post-processing algorithm to reduce the overall complexity, and integrated state-of-the-art high-performance general-purpose GPU to achieve two orders of lower energy consumption compared to previous works. Our work provides the first unambiguous experimental evidence to refute \textit{Sycamore}'s claim of quantum advantage, and redefines the boundary of quantum computational advantage using random circuit sampling.
ABSTRACT Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical simulation time and challenged the claim of first-generation quantum advantage experiments. However, in terms of generating uncorrelated samples, time to solution and energy consumption, previous classical simulation experiments still underperform the Sycamore processor. Here we report an energy-efficient classical simulation algorithm, using 1432 GPUs to simulate quantum random circuit sampling that generates uncorrelated samples with a higher linear cross-entropy score and is 7×\times× faster than the Sycamore 53-qubit experiment. We propose a post-processing algorithm to reduce the overall complexity, and integrate state-of-the-art high-performance general-purpose GPUs to achieve two orders of lower energy consumption compared to previous works. Our work provides the first unambiguous experimental evidence to refute Sycamore’s claim of quantum advantage, and redefines the boundary of quantum computational advantage using random circuit sampling.